Doctors who stare at computer screens rather than look at their patients. Mountains of incomprehensible medical bills and statements. Soaring premiums and deductibles. What do these have in common?

They are the result of a system that does not provide meaningful incentives for innovation, cost-efficiency or higher-quality, consumer-friendly health care.

Of course people want no out-of-pocket costs, low premiums and access to unlimited health care. But after being burned by politicians’ promises, Americans have learned the hard way they can’t have it all. Low out-of-pocket costs are an illusion, an idea that distracts consumers from the real problems of our health-care system.

I blame it on the Affordable Care Act, which has created a system with the worst of both worlds: high premiums, high out-of-pocket costs, and restricted access to providers—all of which place significant barriers to access to care. Enrollees in health exchanges often pay $500 or more a month in premiums for policies with deductibles of $3,000 to $6,000. That can mean spending $12,000 a year before insurance kicks in. Most consumers facing these costs might as well be uninsured.

Lowering their perception of their share of health costs isn’t the answer. Giving them more control over their health spending is.

Fifty years ago, Americans paid nearly half of their health spending out of pocket. Today, they pay just 11%, and only 3% for hospital bills. And because they rely on insurance and government health plans to pay most of their bills, they have no idea what a medical product or procedure actually costs. This lack of price transparency leads to hospitals charging $19 for an aspirin or $300 for an ankle brace that costs $21 at the drugstore.

If patients were able to see and compare the real cost of the products and services, the health-care sector would innovate around things the consumers value: lower costs, more options, and providers who are more responsive to patients’ needs than they are to those of bureaucrats.

In a more functional market, suppliers vie to offer consumers the best products and services at the best price so they can beat their competitors. But the health sector shuts down these market forces by keeping consumers in the dark. The only way we can move to a true market in the health sector is for people to be engaged as active consumers. And that means price visibility and real control over spending.

If price visibility were established, products such as health savings accounts could help more consumers make better-informed choices, save money and drive down costs. HSAs have been proven to reduce total medical costs, boost participation in prevention and wellness programs, and improve access to care.

Many employers jointly fund their employees’ HSAs. And the model also works for public programs. The Healthy Indiana Plan is a successful example of beneficiaries having catastrophic protection while state and beneficiaries jointly fund the account.

Where consumers are cutting back on care, it’s because of the high deductibles in almost all insurance policies offered through the ACA exchanges. Large deductibles on top of high premiums and copayments expose most consumers to huge costs with no health savings account to help pay the bills. While HSAs have been an option in many exchanges, the Obama administration is crippling them with regulations.

People with HSAs and participants in the Indiana Plan think twice about unnecessary emergency-room visits because they know the first dollar comes out of their account. They may opt for an urgent-care clinic or a telemedicine call first. If they have a real emergency, they know they are protected.

Hiding the truth from consumers obscures the real cost of their health care consumption and costs them dearly.

Ms. Turner is president of the Galen Institute, a nonprofit research organization focusing on free-market ideas for health care. Email her at reports@wsj.com.